Rotating Shapes
Rotating shapes means turning a shape around a fixed point called the centre of rotation. The shape keeps its size and shape; only its position changes. To describe a rotation, give the angle and direction, like 90° clockwise.
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What Is Rotation?
- A rotation turns a shape around a fixed point called the centre.
- The shape keeps the same size and shape, only its position changes.
Rotating Shapes Using Tracing Paper
- Place tracing paper on the shape and mark the centre.
- Turn the paper by the given angle in the correct direction.
Rotating Shapes on a Grid
- Draw a line from the centre of rotation to one vertex.
- Turn the line by the given angle, keeping the same distance from the centre.
- Repeat for all vertices and join the points to form the new shape.
Describing a Rotation
- Draw perpendicular bisectors of matching points to find the centre of rotation.
- Measure the angle at the centre from the original point to the rotated point.
Practice Questions
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What is the fixed point around which a shape rotates called?
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The centre of rotation is the fixed point around which the shape rotates.
What does the angle of rotation describe?
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The angle of rotation describes how far the shape is rotated, measured in degrees.
To rotate a shape around a fixed point, does the direction of rotation matter?
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A rotation is the same regardless of the direction of rotation (clockwise or anticlockwise).
If you rotate a shape clockwise, then rotate it another clockwise, what is the final position of the shape?
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A clockwise rotation followed by clockwise adds up to clockwise.
What is equivalent to rotating a shape clockwise?
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A rotation is equivalent to a rotation because subtracting (one full turn) from leaves .
Find the centre of rotation.
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Draw lines connecting corresponding points from the original and rotated shapes and find their perpendicular bisectors. The intersection of these bisectors shows the centre of rotation at (1, 2). The original shape is rotated anticlockwise about (1, 2).
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Interactive Activity
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Students Also Ask
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The centre of rotation is the fixed point that a shape turns around during a rotation. It stays in place while the shape turns about it. When you describe a rotation, you must find this point first, as it tells you where the turn is centred.
To find the centre of rotation, pick a point on the shape and its matching point on the image. Join them with a straight line, then draw the perpendicular bisector. Repeat with a second pair of points. The centre is where the two bisectors cross.
No. For a rotation of 180 degrees, the direction does not matter. A clockwise turn and an anticlockwise turn produce exactly the same image. For any other angle, such as 90 degrees, you must state whether the rotation is clockwise or anticlockwise.
You can rotate a shape using tracing paper. Copy the shape onto the paper, hold the centre still, and turn the paper by the required angle. Or you can use auxiliary lines. Draw a line from the centre to each vertex and rotate each line. Both methods give the same image.
To describe a rotation fully, you need three things. State the angle of rotation, the direction (clockwise or anticlockwise), and the centre of rotation. For example, a full description might read: an anticlockwise rotation of 90 degrees about the point (2,3).